Factual error: When the archangels jump from the helicopter, the "bait" is looking behind him saying he can see the dragon. For a parajumper to look between his legs to view behind himself, he would de-arch and thus de-stabilise himself while travelling at that speed. It would send the jumper into a barrel-roll spin.
Continuity mistake: When Van Zan is showing the dragon tooth to Quinn, the chain that's holding the tooth keeps moving around the entire scene from on his hand to around his hand, etc.
Factual error: At the end of the film, in the battle with the male dragon, what are American traffic lights doing in London?
Plot hole: Given that the dragons overwhelmed the worlds' militaries, the presented ways to bring them down are very gentle, so to speak. The force of impact on the ground would easily be achieved by an air to air or surface to air missile, or an RPG. The crossbow with some explosives has far less strength than a tank shell (weak points or no, the difference is just too great). The dragons are quite tough individually, but would have to succumb to strikes from modern weapons, or even to improvised ancient weapons of modern make. Humans that are able to keep helicopters and M1A2 tanks in running condition would be able to field several weapons that would bring down dragons quickly, effectively and nearly without their own casualties.
Continuity mistake: In the scene where Van Zan shows the dragon tooth to Quinn, Van has a cigar in his hand. But as he lowers his hand, the shot changes and the cigar vanishes.
Continuity mistake: I've seen it in other films but in this one it gets almost ridiculous. Van Zan's beard changes from pretty thick when he's introduced to almost shaved the same day after the first dragon fight then back to thick and fat a couple of days later while in London. Even if we believe he shaved after the dragon fight - which shouldn't be the case since the camera follows him almost the whole time - there's no way it got that fat 2 days later.
Plot hole: They make a big deal about attacking the dragons at twilight. But, apart from the poorly blue-screened shot of McConaughey on top of the tower, there's no sign that the final fight happens anywhere near twilight.
Revealing mistake: It's nice to see that Alex (the helicopter pilot), is able to keep herself in such nice and kempt condition. Look at her... clean, washed and combed hair, makeup, and she's actually got lipstick on in one of the scenes.
Character mistake: When newspapers are flashed on screen to demonstrate how the dragons have destroyed the countries, one of the headlines reads "Europes' capital cities in ruins." It should read "Europe's capital cities in ruins."
Character mistake: After the male dragon has swooped by and destroyed Van Zan's convoy, there is a scene of Alex running through the fire up to him sitting there. After she asks "Where are the soldiers?", the subtitles for the DVD show the lines being spoken "One Pass. He flew over just once." while Van Zan is opening his hand up in a close up to let go of some ash. However nobody is actually saying these words. Turn the volume all the way up, and there is still nobody actually saying this. It's as if these lines were removed without the person in charge of the subtitles being told. Or were removed after he finished the subtitles. (01:11:27)
Factual error: In the scene when they are traveling at night towards London, when they stop at the blockade of burnt out cars and observe the 'London 666' sign, you can partially see that the sign is meant to be a remaining sign for the A5 road in the UK. They are apparently meant to be in Pembury, which is below south London, whereas the A5 goes north of London. Also Pembury is around 30 miles away from London, not 66. (01:07:30)
Revealing mistake: In the final scene, the boy comes riding up the hill towards Quinn. The whole world was supposed to be in ashes but in the background you can see a very green valley.